Precalculus (6th Edition) Blitzer

If there exists a positive number $p$ such that $f\left( t+p \right)=f\left( t \right)$ , function f is periodic. The smallest positive number $p$ for which $f\left( t+p \right)=f\left( t \right)$ is called the period of $t$.
We know that the function $f$ is periodic if there exists a positive value $p$ such that $f\left( t+p \right)=f\left( t \right)$ For all $t$ in the domain of $f$. The smallest positive number $p$ for which $f$ is periodic is called the period of $f$ For example: Sine and cosine functions are periodic functions having a period of $2\pi$. The tangent function is also a periodic function having period of $\pi$